What is the equation in point-slope form of the line passing through (0, 2) and (1, 5)?

1 Answer
smendyka
May 10, 2017

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(5) - color(blue)(2))/(color(red)(1) - color(blue)(0)) = 3/1 = 3#

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

#(y - color(red)(2)) = color(blue)(3)(x - color(red)(0))#

Or

#(y - color(red)(2)) = color(blue)(3)x#

We can also substitute the slope we calculated and the values from the second point in the problem giving:

#(y - color(red)(5)) = color(blue)(3)(x - color(red)(1))#

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